I agree that a homophobic person might be terrified of their own sexuality but they might not.  It could be they fear being gay themselves.  It could be they fear a loved one or close friend is gay.  It could be a fear of the consequences of homosexuality.  It could also just be a fear of something they do not understand.  There was a time when people were very against and very afraid of interracial marriages.  Now, most people, consider this fear misplaced.  It is the same with a person who is homophobic.  Remember that not everyone who disagrees with homosexuality is homophobic and not everyone who is homophobic is a closeted homosexual.

There is an old saying in detective circles that says...he who screams loudest about their innocence is guilty. Now, having said that, I don't believe that saying really holds water but we could perhaps apply it to your question. I really don't think we can say with any degree of certainty a person who is homophobic is necessarily a homosexual.

I believe that the utter disdain in which being gay has traditionally been held in our culture and the contempt one hears heaped on gays (the minister mentioned in post one being a prime example) is so acute that many people have a terrible fear that this might, in fact be they. One post above noted that hatred is complex, which is true; but it is almost always based on fear. The hatred of those whose sexual orientation is not mainstream is based on that fear. Frizzyperm makes a good point that many homophobes are in fact gay themselves; hence the old adage that the best defense is a good offense.

Hate is always based in ignorance and fear. Whether the fear is of one's own sexuality is possible but we cannot judge what is inside someone else. Either way, homophobia, like all predjudice and hatred, caused by some kind of fear: fear of what it means to us (or about us), fear of something we don't understand, fear of something that is unfamiliar to us, and so on. Many prejudices and the fear that inspires them has been taught from birth. 

I think often those who rail the most violently against homosexuality are afraid of their own sexuality. This is not scientific or proven, it is just my opinion. And I'm not saying that all of these people are actually homosexual. What I am saying that they are afraid they might or of what would happen if they were. They are afraid of being different or judged, so they attack first before anyone can attack them.

I need to also said in post #4. Homphobia is not confined to conservatives. Nor are all liberals more self aware and tolerant. Anyone can be a homophobic no matter what their political leanings are. Anyone can be self realized no matter what their political leanings. Lets not add more judgement and division to a topic that is already cause for people to judge one another and divide the community.

So, the answer to the original question is, "Yes, that could be the case, but it isn't always so."

If a person has never dealt with his/her personal sexuality and hasn't worked through identifying his/her beliefs and preferences, is that person a "desparate closeted homosexual" or someone who hasn't progressed down the road to self-understanding and acceptance?

This video has become a very hot topic of late. I agree with post 2. If hate was simple, it would be a lot easier to eradicate. There are a number of social, cultural, religious, and yes, psychological factors behind homophobia, and I suspect many of them are at work in this congregation.

There have been some studies that argue that there is such a connection as you mention.  A discussion of one of these can be found here.

However, this does not by any means prove that all people who are opposed to homosexuality are opposed to it because of fears of their own homosexual tendencies.